lambertw, all branches

[Gil]

I try with Wolfram
W0 (-1.2E-323)
and get the correct answer, ie about -1.2E-323.
Curiously, it offers the possibility to get more digits, two times, but does not show them at the second request.

More strange:
when I ask W0 (-1.2E-324),
I don't get now the expected approximate value -1.2E-324, but
directly zero.

Why this distinction at -1E-323/E-324?